Question

The projection of vector A=i-2j+k onto the direction of B=4i-4j+7k is

Answer 1

Answer:

Explanation:

Given:

$\vec{A} = \hat{i}-2\ \hat{j}+\hat{k}\\\vec{B} = 4\ \hat{i}-4\ \hat{j}+7\ \hat{k}$

Projection is the component of a vector on the other vector. It is nothing but similar to the resolution component of a vector along any one axis.

The projection of a vector over other vector is calculated by the dot product of both the vector.

The projection of vector A on to the direction of vector B is given by:

$\vec{A}\cdot \vec{B}=(\hat{i}-2\ \hat{j}+\hat{k})\cdot(4\ \hat{i}-4\ \hat{j}+7\ \hat{k})\\\Rightarrow \vec{A}\cdot \vec{B}=(\hat{i})\cdot ( 4\ \hat{i})+(-2\ \hat{j})\cdot (-4\ \hat{j})+(\hat{k})\cdot (7\ \hat{k})\\\Rightarrow \vec{A}\cdot \vec{B}=4+8+7\\\Rightarrow \vec{A}\cdot \vec{B}=19$

Hence, the projection of vector A on to the direction of vector B is 19.